Constant solutions of reflection equations and quantum groups

To the Yang-Baxter equation an additional relation can be added. This is thereflection equation which appears in various places, with or without spectralparameter. For example, in factorizable scattering on a half-line, integrablelattice models with non-periodic boundary conditions, non-commutativedifferential geometry on quantum groups, etc. We study two forms of spectralparameter independent reflection equations, chosen by the requirement thattheir solutions be comodules with respect to the quantum group coaction leavinginvariant the reflection equations. For a variety of known solutions of theYang-Baxter equation we give the constant solutions of the reflectionequations. Various quadratic algebras defined by the reflection equations arealso given explicitly.Comment: 31 page